Stochastic complex Ginzburg-Landau equation with space-time white noise

被引：10
|
作者：
Hoshino, Masato [1 ]
Inahama, Yuzuru [2 ]
Naganuma, Nobuaki [3 ]
机构：
[1] Waseda Univ, Sch Fundamental Sci & Engn, Shinjuku Ku, Tokyo 1698555, Japan
[2] Kyushu Univ, Grad Sch Math, Nishi Ku, Fukuoka 8190395, Japan
[3] Osaka Univ, Grad Sch Engn Sci, Toyonaka, Osaka 5608531, Japan
来源：
ELECTRONIC JOURNAL OF PROBABILITY | 2017年 / 22卷
关键词：
stochastic partial differential equation; complex Ginzburg-Landau equation; regularity structure; paracontrolled distribution; renormalization; KPZ EQUATION; ERGODICITY;
D O I：
10.1214/17-EJP125
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We study the stochastic cubic complex Ginzburg-Landau equation with complex-valued space-time white noise on the three dimensional torus. This nonlinear equation is so singular that it can only be understood in a renormalized sense. In the first half of this paper we prove local well-posedness of this equation in the framework of regularity structure theory. In the latter half we prove local well-posedness in the framework of paracontrolled distribution theory.
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页数：68
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